What is the difference between a communicating class and a closed communicating class?
I checked the definition on Wikipedia http://en.wikipedia.org/wiki/Markov_chain#Properties but I couldn't see any difference.
What is the difference between a communicating class and a closed communicating class?
I checked the definition on Wikipedia http://en.wikipedia.org/wiki/Markov_chain#Properties but I couldn't see any difference.
Assume that the only nonzero transitions on the state space $\{a,b,c\}$ are $a\to b$, $b\to a$, $b\to c$, and $c\to c$. Then $\{a,b\}$ and $\{c\}$ are communicating classes, $\{a,b\}$ is not a closed communicating class, and $\{c\}$ is a closed communicating class.